CogSci 131 Levels of analysis

Tom Griffiths

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Levels of analysis

At what level should we try to model human cognition?

Outline

Levels of analysis

Break

The computational level and cognition

David Marr

1982 David Marr 1945-1980

Marr’s three levels

Computation “What is the goal of the computation, why is it

appropriate, and what is the logic of the strategy by which it can be carried out?”

Representation and algorithm “What is the representation for the input and

output, and the algorithm for the transformation?” Implementation

“How can the representation and algorithm be realized physically?”

Analyzing information processing systems

•  What is being computed?

•  Why is it being computed?

What is being computed?

•  Identification of the formal system in operation

•  e.g. cash register: addition – zero element 3+0 = 3

– commutative 3+4 = 4+3 – associative (3+4)+5 = 3+(4+5) –  inverses 4+(-4) = 0

Why is it being computed?

•  Justification of that formal system in terms of function

•  e.g. cash register: addition – buying nothing costs nothing

– order of purchase is irrelevant – grouping does not affect total – purchase+refund is zero

addition is the formal system that satisfies these functional constraints

Computational theory

1.  What is being computed? 2. Why is it being computed?

where 1. is a solution to the computational problem specified by 2.

Analyzing information processing systems

•  What representation?

•  What algorithm?

What representation?

•  Many formal systems solve the same computational problems – e.g. 2+2=4 and 010+010=100

•  What is the mapping between representations and the inputs and outputs to the system?

•  Different representations make certain operations easier or more difficult – e.g. finding powers of 10 or powers of 2

Algorists vs. Abacists

Analyzing information processing systems

•  What is the physical

implementation of the system?

Marr’s three levels

Computation “What is the goal of the computation, why is it

appropriate, and what is the logic of the strategy by which it can be carried out?”

Representation and algorithm “What is the representation for the input and

output, and the algorithm for the transformation?” Implementation

“How can the representation and algorithm be realized physically?”

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Marr’s three levels

Computation “What is the goal of the computation, why is it

appropriate, and what is the logic of the strategy by which it can be carried out?”

Representation and algorithm “What is the representation for the input and

output, and the algorithm for the transformation?” Implementation

“How can the representation and algorithm be realized physically?” Neuroscience

Cognitive psychology

? Computational cognitive science

Computational models can be defined at all three levels

Computation “What is the goal of the computation, why is it

appropriate, and what is the logic of the strategy by which it can be carried out?”

Representation and algorithm “What is the representation for the input and

output, and the algorithm for the transformation?” Implementation

“How can the representation and algorithm be realized physically?” Models based on how neurons compute

Models based on cognitive processes

Models based on optimal solutions to abstract computational problems

An example: Memory

An example: Memory

Implementation “How can the representation and algorithm be

realized physically?” Explaining human memory based on the circuits formed by hippocampal neurons

(Treves & Rolls, 1994)

What computations are supported by different kinds of neurons?

What is the capacity of memory systems made from these neurons?

An example: Memory

Representation and algorithm “How can the representation and algorithm be

realized physically?” Explaining human memory based on the representation of items with binary features, and a rule for determining familiarity

Item 1: 00101011

Item 2: 01010010

Item 3: 11011010

…

Old probe: 00101011

New probe: 01111011

Activate items with matching features

Familiarity is sum of all activation

(e.g. Hintzman, 1988)

An example: Memory

Computation “How can the representation and algorithm be

realized physically?” Explaining human memory as an optimal solution to the statistical problem of identifying items likely to be needed again

(Anderson, 1990)

Marr’s three levels

•  Are three levels enough?

•  Are these the right set of three levels for guiding investigation of cognition?

•  Is one level more important than the others?

Break

Up next: The computational level and cognition

Is one level more important?

•  Marr: the computational level is most important, imposing the most constraints

Is one level more important?

•  Marr: the computational level is most important, imposing the most constraints

•  Only the computational level gives a purposive (vs. mechanistic) explanation

“...trying to understand perception by studying only neurons is like trying to understand bird flight by studying only feathers: It just cannot be done. In order to understand bird flight, we have to understand aerodynamics; only then do the structure of feathers and the different shapes of birds' wings make sense.”

Different kinds of explanation

•  Mechanistic: how? – algorithm –  implementation

•  Purposive: why?

–  function/problem – optimal solution

Is one level more important?

•  The computational level is also the one at which it doesn’t matter whether we’re studying humans or machines…

•  Provides the potential for insights to cross from one discipline to another

input output input output input output

An example: Memory

Computation “How can the representation and algorithm be

realized physically?” Explaining human memory as an optimal solution to the statistical problem of identifying items likely to be needed again

(Anderson, 1990)

Questions

•  How does one go about conducting a computational-level analysis?

•  What is the equivalent of aerodynamics for cognition?

•  Are there any dangers of pursuing explanations at the computational level?

Questions

•  How does one go about conducting a computational-level analysis?

•  What is the equivalent of aerodynamics for cognition?

•  Are there any dangers of pursuing explanations at the computational level?

Five easy steps

Step 1: Find an interesting aspect of cognition

Step 2: Identify the underlying computational problem

Step 3: Work out the optimal solution to that problem

Step 4: See how well that solution corresponds to human behavior (do some experiments!)

Step 5: Iterate Steps 2-5 until it works

Optimization

•  The key to producing a purposive explanation •  Provides a potential connection between

function and behavior, if there’s a reason to believe that behavior should be optimal –  if people solve a problem badly, then that’s not

the answer to a “why” question •  Also the source of the connection to other

disciplines… convergent evolution! – good solutions apply across different systems

Optima for animals

•  Explanations based on optimization appear in mathematical biology – structure of organisms – behavior

•  Adaptation is typically explicitly evolutionary (people can learn too)

Questions

•  How does one go about conducting a computational-level analysis?

•  What is the equivalent of aerodynamics for cognition?

•  Are there any dangers of pursuing explanations at the computational level?

Cognitive aerodynamics

•  What is the mathematical theory that characterizes optimal solutions for the computational problems that people face?

•  Depends on the computational problem… – deductive reasoning: logic –  inductive reasoning: statistics

•  How are the computational problems that people face best characterized?

Questions

•  How does one go about conducting a computational-level analysis?

•  What is the equivalent of aerodynamics for cognition?

•  Are there any dangers of pursuing explanations at the computational level?

Five easy steps

Step 1: Find an interesting aspect of cognition

Step 2: Identify the underlying computational problem

Step 3: Work out the optimal solution to that problem

Step 4: See how well that solution corresponds to human behavior (do some experiments!)

Step 5: Iterate Steps 2-5 until it works This can be dangerous… what if people just aren’t solving a

the problem in an optimal way?

Bad purposive explanations…

•  Some properties of the structure of organisms are explained by their history, not their function – e.g. male nipples

•  Some aspects of human cognition are going to be explained by the structure of our brains and our cognitive capacities –  looking for purposive explanations everywhere will

cause trouble… it’s a strategy rather than a rule

Levels of analysis

At what level should we try to model human cognition?

computational problem

algorithm

implementation

Thursday

•  The start of rules and symbols… –  read Haugeland on formal systems –  read AIMA for background on logic